Proof theory for theories of ordinals. I: Recursively Mahlo ordinals

DOI10.1016/S0168-0072(03)00020-4zbMath1032.03049MaRDI QIDQ1400597

Toshiyasu Arai

Publication date: 13 August 2003

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

zbMATH Keywords

ordinal diagramsreflecting ordinalsproof-theoretic ordinalsMahlo ordinals

Mathematics Subject Classification ID

Second- and higher-order arithmetic and fragments (03F35) Recursive ordinals and ordinal notations (03F15)

Related Items (12)

Proof theory for theories of ordinals. II: \(\Pi_{3}\)-reflection ⋮ Well-Ordering Principles in Proof Theory and Reverse Mathematics ⋮ Wellfoundedness proofs by means of non-monotonic inductive definitions I: Π₂⁰-operators ⋮ Epsilon substitution for \(ID_1\) via cut-elimination ⋮ Relativized ordinal analysis: the case of power Kripke-Platek set theory ⋮ Wellfoundedness proofs by means of non-monotonic inductive definitions. II: First order operators ⋮ Cut-elimination for \(\omega_{1}\) ⋮ Ordinal analysis by transformations ⋮ A Buchholz derivation system for the ordinal analysis of KP + Π₃-reflection ⋮ Analytic combinatorics, proof-theoretic ordinals, and phase transitions for independence results ⋮ Epsilon substitution method for \([\Pi^0_1,\Pi^0_1\)-FIX] ⋮ Cut-Elimination for SBL

Cites Work

• Proof-theoretic analysis of KPM
• Proof theory. 2nd ed
• Ordinal diagrams for recursively Mahlo universes
• Zur Beweistheorie Der Kripke-Platek-Mengenlehre Über Den Natürlichen Zahlen
• A formalization of the theory of ordinal numbers
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